The CISO of the ABC company is considering how to increase the strength of employee passwords. Currently, passwords must be eight characters, they must be case-sensitive, and they must contain at least two numbers.

a. Calculate the size of the search space of possible passwords given the current password requirements.

b. Calculate the size of the search space of possible passwords if the current password requirements were changed so that they must contain at least two special characters (e.g., $, #, @, etc.) from a list of 33 commonly available symbols.

c. Calculate the size of the search space of possible passwords if the current password requirements were changed so that passwords must be 12 characters long.

d. Which modification to the current password requirements (adding the requirement to include special symbols or increasing the length from 8 to 12) increases the strength of the password the most?

e. Which modification do you recommend? Why?